Instanton Liquid Research Articles

Possible scenario of dynamical chiral symmetry breaking in the interacting instanton liquid model

We compute the vacuum energy density as a function of the quark condensate in the interacting instanton liquid model (IILM) and examine the pattern of dynamical chiral symmetry breaking from its behavior around the origin. This evaluation is performed by using simulation results of the IILM. We find that chiral symmetry is broken in the U(1)A anomaly assisted way in the IILM with three-flavor dynamical quarks. We call such a symmetry breaking the anomaly-driven breaking, which is one of the scenarios of chiral symmetry breaking proposed in the context of the chiral effective theories. We also find that the instanton-quark interaction included in the IILM plays a crucial role for the anomaly-driven breaking by comparing the full and the quenched IILM calculations. Published by the American Physical Society 2024

Confinement in QCD and generic Yang-Mills theories with matter representations

We derive the low-energy limit of quantum chromodynamics (QCD) and provide evidence that in the 't Hooft limit, i.e. for a very large number of colors and increasing 't Hooft coupling, quark confinement is recovered. The low energy limit of the theory turns out to be a non-local Nambu–Jona-Lasinio (NJL) model. The effect of non-locality, arising from a gluon propagator that fits quite well to the profile of an instanton liquid, is to produce a phase transition from a chiral condensate to an instanton liquid, as the coupling increases with lower momentum. This phase transition suffices to move the poles of the quark propagator to the complex plane. As a consequence, free quarks are no longer physical states in the spectrum of the theory.

Multi-fractional instantons in SU(N) Yang-Mills theory on the twisted T4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{T}}^4 $$\\end{document}

We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus T4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{T}}^4 $$\\end{document} with ’t Hooft twisted boundary conditions. These instantons possess topological charge Q=rN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ Q=\\frac{r}{N} $$\\end{document}, where 1 ≤ r < N. To implement the twist, we employ SU(N) transition functions that satisfy periodicity conditions up to center elements and are embedded into SU(k) × SU(ℓ) × U(1) ⊂ SU(N), where ℓ + k = N. The self-duality requirement imposes a condition, kL1L2 = rℓL3L4, on the lengths of the periods of T4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{T}}^4 $$\\end{document} and yields solutions with abelian field strengths. However, by introducing a detuning parameter ∆ ≡ (rℓL3L4 – kL1L2)/L1L2L3L4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{L_1{L}_2{L}_3{L}_4} $$\\end{document}, we generate self-dual nonabelian solutions on a general T4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbbm{T}}^4 $$\\end{document} as an expansion in powers of ∆. We explore the moduli spaces associated with these solutions and find that they exhibit intricate structures. Solutions with topological charges greater than 1N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N} $$\\end{document} and k ≠ r possess non-compact moduli spaces, along which the O∆\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left(\\Delta \\right) $$\\end{document} gauge-invariant densities exhibit runaway behavior. On the other hand, solutions with Q=rN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ Q=\\frac{r}{N} $$\\end{document} and k = r have compact moduli spaces, whose coordinates correspond to the allowed holonomies in the SU(r) color space. These solutions can be represented as a sum over r lumps centered around the r distinct holonomies, thus resembling a liquid of instantons. In addition, we show that each lump supports 2 adjoint fermion zero modes.

Gluons, light and heavy quarks in the instanton vacuum

In this paper, we put our focus towards describing the nonperturbative effects in the properties of hadrons made from the light-heavy and the heavy–heavy quarks in the framework of Instanton Liquid Model (ILM) of QCD vacuum. The main features of ILM and its applicability in the heavy quark sector are briefly discussed. The properties of gluonic systems, the light and heavy quark correlators in the instanton background are also analyzed. We demonstrate that the consideration of both, perturbative and nonperturbative, gluon effects in the instanton background for a single heavy quark leads to the mass shift due to the direct-instanton nonperturbative and ILM modified perturbative contributions, respectively. For the interacting heavy quark and heavy anti-quark, the potential consists of the direct instanton-induced part and the one-gluon exchange (OGE) perturbative part. OGE interactions are screened at large distances due to the nonperturbative dynamics. The estimation of instanton contributions in the phenomenological Cornell-type potential model is presented. In relation to the experimental data, the charmonium properties, the role of instanton effects in their spectra and transitions are discussed. The main features of heavy-light quark systems in the instanton generated background are also discussed. As an example, we consider the process of pion emissions by the exited heavy quarkonium. We show that there is a sizable correction ([Formula: see text]) to the dipole approximation for the process [Formula: see text].

Importance of confinement in instanton induced potential for bottomonium spectroscopy

Mass spectra of bottomonium states are computed using the Instanton Induced potential obtained from Instanton Liquid Model for QCD vacuum and incorporating a stronger confinement term. Spin dependent interactions through confined one gluon exchange potential are incorporated to remove the mass degeneracy. The mass spectra of the bbar{b} states up to 4S states are found to be in good agreement with the values reported by PDG(2020). Mixing of nearby isoparity states are also studied. We found the state varUpsilon (10{,}860) as an admixture of 5^3S_1 and 6^3D_1 Upsilon states with mixing angle theta = 39.98^{circ } and the mixed state di-leptonic decay width is found to be 0.25 keV as against the width of 0.31 pm 0.07 keV reported by PDG. Further the state varUpsilon (11{,}020) is also found to be the admixture of 6^3S_1 and 5^3D_1 Upsilon states with the mixing angle theta = 51.69^{circ } and the di-leptonic decay width of the mixed state is obtained as 0.14 keV which is very close to the width of 0.13 pm 0.03 keV reported by PDG. Present results indicates that addition of confinement to the instanton potential is crucial for the determination of the mass spectroscopy of heavy hadrons.

Quark Models of the Nucleon–Nucleon Interaction

The present chapter aims to provide a review on the relevance of quark degrees of freedom in the description of the nucleon-nucleon and, in general, of the baryon-baryon interaction. After an historical introduction, the second section of the chapter will be dedicated to the first attempts to describe the short-range part of the NN potential in the so-called quark potential models. Here the importance of the symmetries of the 6-quark system will be emphasized. Then, we will discuss the concept of the constituent quark mass as originated by the breakdown of the chiral symmetry, in line with the articles of ~\citep{MANOHAR1984189} and the Instanton Liquid Model of ~\citep{Diakonov:2002fq}, and its consequences on the quark-quark interaction due to the presence of the Goldstone boson exchanges. Once the full quark-quark interaction is established, the description of the bound states (deuteron), the scattering states of the NN system and nuclear matter in constituent quark models will be addressed. In this part a discussion of the influence of $N\Delta$, $\Delta\Delta$ or $NN^*$ components will be included. The rest of the chapter will be devoted to the extension of the model to other baryon-baryon system, namely the triton, hyperon-hyperon and nucleon-antinucleon systems, and references to other possible descriptions of the NN interaction in terms of quark degrees of freedom ( bag models). The chapter will end with a conclusion remarks where the success and limitations of the model described above will be summarized.

Heavy quarkonium potential at nonzero temperature in the instanton liquid model

Within the framework of the instanton Liquid Model (ILM) we evaluate the heavy quark [Formula: see text] potential at finite temperature. The potential in the ILM has two components: direct instantons contribution and the ILM modified one-gluon exchange contribution. The dynamical ”electric” mass [Formula: see text], which was generated by rescattering of the gluons from the ILM instantons, was taken into account.

Heavy Quarkonium and Dynamical Gluon Mass at Non-zero Temperature in Instanton Vacuum Model

In the framework of the Instanton Liquid Model we evaluate the heavy quark $\bar{Q}Q$ potential at nonzero temperature $T$. The potential has two components: contribution due to direct interaction with instantons, and the modification of the one-gluon exchange contribution via instanton-generated dynamical \char`\"{}electric\char`\"{} gluon mass $M_{el}(q,T)$. We conclude that the nonperturbative ILM contributions to the $Q\bar{Q}$ potential have pronounced temperature dependence, which might be tested in phenomenological analyses of charmonia production data.

Instanton liquid properties from lattice QCD

We examined the instanton contribution to the QCD configurations generated from lattice QCD for NF = 0, NF = 2 + 1 and NF = 2 + 1 + 1 dynamical quark flavors from two different and complementary approaches. First via the use of Gradient flow, we computed instanton liquid properties using an algorithm to localize instantons in the gauge field configurations and studied their evolution with flow time. Then, the analysis of the running at low momenta of gluon Green’s functions serves as an independent confirmation of the instanton density which can also be derived without the use of the Gradient flow.

Instanton dominance over αs at low momenta from lattice QCD simulations at Nf = 0, Nf = 2 + 1 and Nf = 2 + 1 + 1

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for αs in the symmetric momentum subtraction scheme (MOM) for large-volume lattice simulations. We have exploited quenched gauge field configurations, Nf = 0, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with Nf = 2 + 1 and Nf = 2 + 1 + 1 dynamical flavors (domain wall and twisted-mass fermions, respectively). We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination of phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing. We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, ΛQCD, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions.

Gluons, Heavy and Light Quarks in the QCD Vacuum

We are discussing the properties of the QCD vacuum which might be important especially for the understanding of hadrons with small quark core size ~ 0:3 fm: We assume that at these distances the QCD vacuum can be described by the Instanton Liquid Model (ILM). At larger distances, where confinement is important, ILM should be extended to Dyons Liquid Model (DLM). The ILM has only two free parameters, average instanton size ρ ≈ 0:3 fm and average inter-instanton distance R ≈ 1 fm, and can successfully describe the key features of light hadron physics. One of the important conceptual results was prediction of the momentum dependent dynamical quark mass M ~ (packing f raction)1/2 ρ-1 ≈ 360 MeV, later confirmed numerically by evaluations in the lattice. The estimates show that gluon-instanton interaction strength is also big and is controlled by the value of dynamical gluon mass Mg ≈ M. Heavy quarks interact with instantons much weaker. The heavy quark-instanton interaction strength is given by ΔmQ ~ packing fraction ρ-1 ≈ 70 MeV: Nevertheless, the direct instanton contribution to the colorless heavy-heavy quarks potential is sizable and must be taken into account. At small distances, where one-gluon exchange contribution to this potential is dominated, we have to take into account dynamical gluon mass Mg. Also, instantons are generating light-heavy quarks interactions and allow to describe the nonperturbative effects in heavy-light quarks systems.

Holographic D instanton liquid and chiral transition

In the presence of uniform D-instanton charges, quarks can be confined although gluons are not, because baryon vertices are allowed due to the net repulsive force on the on the probe D-branes. Since there is no scale in the geometry itself apart from the horizon size, there is no Hawking-Page transition. As a consequence, the D7 brane embedding can encode the effect of the the finite temperature as well as finite baryon density even for low temperature. The probe D-brane embedding, however, undergoes a chiral phase transition according to the temperature and density parameter. We studied such phase transitions and calculated the constituent quark mass, chiral condensation and the binding energy of baryons as function of the density. The baryon vertex melting is identified as the quark deconfinement. We draw phase diagram according to these transitions.

Chiral symmetry in the low-energy limit of QCD at finite temperature

We derive a non-local Nambu-Jona-Lasinio model from QCD with a form factor exactly obtained in the infrared limit. With this model, having all the parameters properly fixed through those of QCD, we consider the case of finite temperature and compute the solution of the gap equation at small temperature and small momenta and zero chemical potential. Taking the quark masses to be zero, it is proved that the theory undergoes a phase transition with a critical temperature exactly determined. These results prove unequivocally that the picture of the vacuum of QCD as a liquid of instantons is a very good approximation.

Axion cosmology revisited

The misalignment mechanism for axion production depends on the temperature-dependent axion mass. The latter has recently been determined within the interacting instanton liquid model, and provides for the first time a well-motivated axion mass for all temperatures. We reexamine the constraints placed on the axion parameter space in the light of this new mass function. Taking this mass at face value, we find an accurate and updated constraint ${f}_{a}\ensuremath{\le}2.8(\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{10}^{11}\text{ }\text{ }\mathrm{GeV}$ or ${m}_{a}\ensuremath{\ge}21(\ifmmode\pm\else\textpm\fi{}2)\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}$ from the misalignment mechanism in the classic axion window (thermal scenario). However, this is superseded by axion string radiation which leads to ${f}_{a}\ensuremath{\lesssim}{3.2}_{\ensuremath{-}2}^{+4}\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }\text{ }\mathrm{GeV}$ or ${m}_{a}\ensuremath{\gtrsim}{0.20}_{\ensuremath{-}0.1}^{+0.2}\text{ }\text{ }\mathrm{meV}$. In this analysis, we take care to precisely compute the effective degrees of freedom and, to fill a gap in the literature, we present accurate fitting formulas. We solve the evolution equations exactly, and find that analytic results used to date generally underestimate the full numerical solution by a factor 2--3. In the inflationary scenario, axions induce isocurvature fluctuations and constrain the allowed inflationary scale ${H}_{I}$. Taking anharmonic effects into account, we show that these bounds are actually weaker than previously computed. Considering the fine-tuning issue of the misalignment angle in the whole of the anthropic window, we derive new bounds which open up the inflationary window near ${\ensuremath{\theta}}_{a}\ensuremath{\rightarrow}\ensuremath{\pi}$. In particular, we find that inflationary dark matter axions can have masses as high as $0.01--1\text{ }\text{ }\mathrm{meV}$, covering the whole thermal axion range, with values of ${H}_{I}$ up to ${10}^{9}\text{ }\text{ }\mathrm{GeV}$. Quantum fluctuations during inflation exclude dominant dark matter axions with masses above ${m}_{a}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{meV}$.

10.1007/s11497-008-1002-1

The thermal and quark/baryon chemical potential dependences of quark condensate and masses of $\pi$- and $\sigma$-mesons are studied in the instanton model of the QCD vacuum in precritical region. The impact of phonon-like excitations of instanton liquid on the characteristics of $\sigma$-meson in such an environment is also examined.

The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Zero temperature calibrations and numerical framework

This is the first in a series of papers which ultimately aims on improving on the present estimates on the axion mass by modelling the topological non-perturbative QCD dynamics. Axions couple to instantons and their mass is set by the topological susceptibility whose temperature dependence we estimate with the interacting instanton liquid model (IILM). Since accurate finite temperature instanton calculations have problems and do not consider fluctuations in the topological charge, we develop an improved grand canonical version of the IILM to study topological fluctuations in the quark gluon plasma. In this first paper we will calibrate the model against the topological susceptibility at zero temperature, in the chiral regime of physical quark masses.

The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Strongly associating fluids and biased Monte Carlo

This is the second in a series of papers that investigates the topological susceptibility in the interacting instanton liquid model (IILM); it deals with the technical issues relating to the Monte Carlo simulations that are specific to finite temperature. The IILM reduces field theory to a molecular dynamics description, and for ‘physical’ quark masses the system behaves like a strongly associating fluid. We will argue that this is a generic feature for very light Dirac quarks in a non-trivial background, described in the semi-classical approach. To get rid of unnecessary complications, we will present the ideas of biased Monte Carlo, and implement the transition probabilities, for a toy model.

The topological susceptibility from grand canonical simulations in the interacting instanton liquid model: Chiral phase transition and axion mass

This is the last in a series of papers on the topological susceptibility in the interacting instanton liquid model (IILM). We will derive improved finite temperature interactions to study the thermodynamic limit of grand canonical Monte Carlo simulations in the quenched and unquenched case with light, physical quark masses. In particular, we will be interested in chiral symmetry breaking. The paper culminates by giving, for the first time, a well-motivated temperature-dependent axion mass. Especially, this work finally provides a computation of the axion mass in the low temperature regime, m a 2 f a 2 = 1.46 × 10 − 3 Λ 4 1 + 0.50 T / Λ 1 + ( 3.53 T / Λ ) 7.48 . It connects smoothly to the high temperature dilute gas approximation; the latter is improved by including quark threshold effects. To compare with earlier studies, we also provide the usual power-law m a 2 = α a Λ 4 f a 2 ( T / Λ ) n , where Λ = 400 MeV , n = 6.68 and α = 1.68 × 10 − 7 .

One method for the self-consistent determination of instanton liquid parameters

The possibility of self-consistently determining instanton liquid parameters with optimal pseudoparticle configurations is discussed. The estimate of repulsive pseudoparticle-interaction weakening is obtained. A comparison of different ensembles of pseudoparticles is made.

Modified action for light quarks in the instanton vacuum

The procedure of averaging in an instanton medium in quarks with any number of flavors is discussed. It is shown that the effect of the instanton medium is equivalent to an interaction of light quarks with dynamically generated mass (four-quark interaction Nf = 2) and massless bosonic spinor fields (ghosts). The fact that the instanton liquid is dilute makes it possible to use perturbation theory.